Friday, November 14, 2008

Once again into the E = K fray!

I'm reading Comesana and Kantin's forthcoming PPR piece, "Is Evidence Knowledge?" (here). They argue that E = K is incompatible with the existence of Gettier cases and that it is incompatible with closure. I don't have time for the second complaint, but I'd like to quickly address the first.

They attack: (E = K 1): The proposition that p justifies S in believing that q only if S knows p.

They allege that (E = K 1) is incompatible with Gettier cases, but focus on a single case, Coins:
You are waiting to hear who among the candidates got a job.
You hear the secretary say on the telephone that Jones got the job.
You also see Jones empty his pockets and count his coins: he has
ten. You are, then, justified in believing that Jones got the job and
also that Jones has ten coins in his pocket. From these two beliefs
of yours, you infer the conclusion that whoever got the job has ten
coins in his pocket. Unbeknownst to you, the secretary was wrong
and Jones did not get the job; in fact, you did. By chance, you
happen to have ten coins in your pocket

Minor point. Not every Gettier case has the structure of coins, so even if you can't say that there's a justified, true belief that fails to constitute knowledge in this case it hardly follows that Gettier cases as such are ruled out by (E = K 1). Less minor point. What's the problem supposed to be? They say, "What is justified in Coins is the belief that whoever got the job has ten coins in his pocket. But what justifies the subject in having that belief is (in part) his false belief that Jones got the job". Minor point. If this is a datum that our theories of evidence need to accommodate, then on any view on which our evidence consists of facts or propositions, there cannot be Gettier cases. Less minor point. Among the things that the subject knows is that the subject has this belief, the belief is well supported by the evidence, etc... It's hardly obvious that (E = K 1) rules out the false belief from playing some justificatory role. What it rules out is just this: that the content of the false belief is a part of the subject's evidence. In other words, it seems that C & K are really offering this argument:

(1) According to E = K, there are no false propositions that are included in a subject's evidence.
(2) If there are no false propositions included in someone's evidence, Coins is not a Gettier case.
(3) Coins is a Gettier case.
(C1) There are false propositions included in someone's evidence.
(C2) We must reject (E = K 1).

I'd reject the factivity of 'knows' and save E = K that way. Just kidding. Alan Hazlett has dibs on that move. While it's true that there cannot be false propositions included in someone's evidence if (E = K 1) is true, I distinctly remember asking a while back if _anyone_ thought that there could be false propositions included in someone's evidence and the response seemed to be that there couldn't. That's hardly an argument, but there's something very strange to this objection. Now, C & K say that, "there is no argument that we can think of to the effect that your (false) belief that Jones got the job plays no part whatsoever in justifying you in thinking that whoever got the job has ten coins in his pocket". But there is. It's the argument that says that false propositions cannot be included in your evidence.

Now, it might be a bad argument, but to paraphrase, bad arguments are a kind of argument. So, here it is. One problem with saying that there could be false propositions emerges if we think about these exchanges:

Scarlet: Do they have solid evidence against Mustard?
Green: Yes. They have all sorts of evidence against him; namely, that he was the last one to see the victim alive, that his alibi did not check out, that his fingerprints were on the murder weapon, and that he had written a letter to his brother containing details only the killer could have known.

Later, Peacock and Plum talk things over:
Peacock: How strong is their evidence against Mustard?
Plum: I've heard that the evidence is pretty strong. But, if Mustard’s fingerprints are not really on the murder weapon, his alibi checks out, he was not the last one
seen with the victim, and there is nothing in his letters that actually indicate he had any insider’s knowledge of the killings, that is perfectly consistent with the evidence they do have.

It seems that in speaking to Plum and Green contradict one another. The natural explanation for this is that if it really is part of the evidence that Mustard’s fingerprints are on the murder weapon, then it is true that his fingerprints are on the murder weapon. So, if that it is right, an assertion of the form ‘His evidence is that p, q, and r’ entails that p, q, and r are true.

The presentation of the example in Gettier's original paper:
Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition:

(d) Jones is the man who will get the job, and Jones has ten coins in his pocket.

Smith's evidence for (d) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago. Proposition (d) entails:

(e) The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is then true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith's pocket, while Smith does not know how many coins are in Smith's pocket, and bases his belief in (e) on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job.


Mike Almeida said...

I distinctly remember asking a while back if _anyone_ thought that there could be false propositions included in someone's evidence and the response seemed to be that there couldn't.
But what if your false beliefs entailed something true, and you knew this? Consider the inference P |- ~P, (to give it a name, call it 'quasi-valid'). The falsity of the premises quarantees the truth of the conclusion; in other words, it is impossible for the premises of this argument to be false and the conclusion false also. To consider another, (P -> Q) |- ~(P & Q), which is also quasi-valid. If the premises are false then the conclusion must be true. So it is difficult to see why false propositions--such as those that occur in quasi-valid arguments--are not evidential. If you throw these into your evidence base, you can draw some true conclusions using quasi-valid inferences.

Clayton said...

It's an interesting case, but I'm not quite sure I follow the details.

Are you suggesting that:

(a) You know that the belief that p is false and entails some other proposition.

(b) You believe p not knowing that ~p but knowing that p entails something else?

If it's (a), you can say that there's something you know (i.e., that the belief that p is false) and what you know is evidence for something else.

If it's (b), I don't see how you could draw q-valid inferences.

Mike Almeida said...

You asked" 'could there be false propositions in one's evidence base'? I say, yes, I think there could be, so long as the false proposition had some interesting logical relation to a true proposition. Let P be such a proposition. It is P, not my belief that P is false, that enters into the quasi-valid inference, P |- ~P. You ask: why is P in your evidence base, it's false. I say: I know, I include false propositions in my evidence base because I can derive other true propositions from the false ones. I do not derive true propositions from my belief that P is false. I derive it from the false proposition, P.
I'm assuming that we are not assuming a priori that one's evidence based could not include a false proposition. I'm assuming that, just as one knows that one's evidence based includes true propositions, one might knows that one's base include some false propositions.

Clayton said...


I'm still not sure what to make of your examples. They are interesting, but one of the oddities of these examples is that if they are supposed to involve inferential justification, it seems that the believer would have to have both beliefs for the inference to transmit justification. And, it seems that it's hard to imagine how that could be.